Chapter 152 Electronic structure calculations for molecules containing lanthanide atoms

Data-driven approaches offer great potential for accelerating abinitio electronic structure calculations of molecules and materials, but their transferability is often limited due to the vast amount of data needed for training, including the need to fine-tune universal models for each specific system to be studied. Here, we demonstrate how contributions from system-specific electronic structure machine learning (ESML) models may be combined ("stitched") to deliver density matrices of entire systems of interest, improving the initial guess for the self-consistent field cycle and delivering gains in computational efficiency. The "stitching" of density matrices is demonstrated for sequential calculations, such as geometry optimization and molecular dynamics, and we show that the synergistic use of ESML models and density matrix extrapolation algorithms can accelerate standard computational calculations. The algorithms are demonstrated for test cases relating to water clusters and a methane clathrate cage, with the benefits discussed. The future opportunities for hybrid quantum mechanical and ML (QM/ML), and also ML/ML paradigms, are broad-ranging with significant computational speed-up attainable.

QWalk: A quantum Monte Carlo program for electronic structure

Advantages and disadvantages of two approaches to electronic structure calculations of molecules using the NDDO approximation are revealed.

The choice of Gaussian type basis sets for electronic structure calculations of molecules is discussed in detail for treatments on the SCF and Cl level. This article is organized in the following sections : I. Introduction, II. Mathematical foundation of the LCAO-MO method, III. Basis sets of first and second row atoms in SCF calculations, IV. Transition metals, V. Beyond-Hartree-Fock calculations, VI. Summary.Detailed proposals are made for the choice of basis sets at various levels of computational expense.

Electronic structure calculations for molecules adsorbed on the surface of ionic crystals

The pseudopotential method has grown as a powerful tool for multiphase fluid flow simulations within the lattice Boltzmann method framework. We consider that due to its simplicity and computational efficiency, the pseudopotential method could be explored also inside the framework of more traditional Computational Fluid Dynamic methods such as Finite Difference, Finite Volume or Finite Element methods. Following this idea, in this work we start from the macroscopic equations resulting from the pseudopotential lattice Boltzmann method and discretize it by a simple Finite Difference scheme. This pseudopotential based finite difference method is then tested in different benchmark problems such as a planar interface, a smooth droplet oscillation, and a single droplet evaporation. Excellent results were obtained in all tests. One of the advantages of the proposed method is that mesh refinement is straightforward, and converged solutions can be used as a tool of validation for the lattice Boltzmann method. Results indicate that the pseudopotential method is suitable to be used with standard discretization methods such as Finite Difference and that in future works more robust discretizations can be used to further enhance the pseudopotential method application.

We have studied transition-metal 3d-oxygen 2p lattice models, where full degeneracy of transition-metal 3d and oxygen 2p orbitals and on-site Coulomb and exchange interactions between 3d electrons are taken into account, by means of a spin- and orbital-unrestricted Hartree-Fock (HF) approximation. The electronic-structure parameters deduced from the cluster-model analyses of the photoemission spectra are used as input. We have applied this method to perovskite-type 3d transition-metal oxides, which exhibit various electrical and magnetic properties. It is shown that the HF results can explain the ground-state properties of insulating oxides. The relationship between spin- and orbital-ordered solutions and the Jahn-Teller-type and ${\mathrm{GdFeO}}_{3}$-type distortions in R${\mathrm{TiO}}_{3}$, R${\mathrm{VO}}_{3}$, R${\mathrm{MnO}}_{3}$, and R${\mathrm{NiO}}_{3}$ (R is a rare earth atom or Y) is extensively studied. Single-particle excitation spectra calculated using Koopmans' theorem give us an approximate but relevant picture on the electronic structure of the perovskite-type 3d transition-metal oxides. As a drawback, the HF calculations tend to overestimate the magnitude of the band gap compared with the experimental results and to predict some paramagnetic metals as antiferromagnetic insulators. \textcopyright{} 1996 The American Physical Society.

The current progress in describing rare-earth-based magnets' electronic structure and magnetic properties is discussed. We use several currently popular electronic structure methods to show the typical values of critical parameters that define the physics of RECo5 (RE = rare earth atom) materials. The magnetic moments and magnetic anisotropy of 4f atoms are obtained using several approaches, including anisotropic 4f-charge density-constrained DFT and DFT+HI methods. We also suggest the introduction of "penalty" functional for obtaining correct variational total energy in the traditional Hund's rule-constrained DFT-based techniques. The applicability and future extensions are discussed. The proposed combination of methods is potentially suitable for high-throughput computational searches of new rare-earth-containing magnetic materials.

The need for cost optimization in a broad sense constitutes the basis of operation of every enterprise. In the case of IT structure, which is present in almost every field of activity these days, one of the most commonly applied technologies leading to good cost-to-profit adjustment is virtualization. It consists in locating several operational systems with IT systems on a single server. In order for such optimization to be carried out correctly it has to be strictly controlled by means of allocating access to resources, which is known as performance isolation. Modern virtualizers allow to set up this allocation in quantitative terms (the number of processors, size of RAM, or disc space). It appears, however, that in qualitative terms (processor's time, RAM or hard disc bandwidth) the actual allocation of resources does not always correspond with this configuration. This paper provides an experimental presentation of the achievable level of performance isolation of the Hyper-V virtualizer.

A novel method is presented that significantly reduces the computational bottleneck of executing high-level, electronic structure calculations of the energies and their gradients for a large database that adequately samples the configuration space of importance for systems containing more than four atoms that are undergoing multiple, simultaneous reactions in several energetically open channels. The basis of the method is the high-degree of correlation that generally exists between the Hartree-Fock (HF) and higher-level electronic structure energies. It is shown that if the input vector to a neural network (NN) includes both the configuration coordinates and the HF energies of a small subset of the database, MP4(SDQ) energies with the same basis set can be predicted for the entire database using only the HF and MP4(SDQ) energies for the small subset and the HF energies for the remainder of the database. The predictive error is shown to be less than or equal to the NN fitting error if a NN is fitted to the entire database of higher-level electronic structure energies. The general method is applied to the computation of MP4(SDQ) energies of 68,308 configurations that comprise the database for the simultaneous, unimolecular decomposition of vinyl bromide into six different reaction channels. The predictive accuracy of the method is investigated by employing successively smaller subsets of the database to train the NN to predict the MP4(SDQ) energies of the remaining configurations of the database. The results indicate that for this system, the subset can be as small as 8% of the total number of configurations in the database without loss of accuracy beyond that expected if a NN is employed to fit the higher-level energies for the entire database. The utilization of this procedure is shown to save about 78% of the total computational time required for the execution of the MP4(SDQ) calculations. The sampling error involved with selection of the subset is shown to be about 10% of the predictive error for the higher-level energies. A practical procedure for utilization of the method is outlined. It is suggested that the method will be equally applicable to the prediction of electronic structure energies computed using even higher-level methods than MP4(SDQ).

Numerical simulation of power transmission lines

A comparison of the central processing unit (CPU) time and storage requirements for the parallel and deductive fault simulation techniques is presented. Versions of a parallel and deductive simulator were implemented and the comparison performed on an IBM System/360 Model 67 by simulating representative circuits including shift registers, sequencers, counters, two memory units, and a processor. The results indicate that the deductive technique requires less CPU time for "loosely sequential" circuits or circuits having large numbers of simulated faults (e.g., >1000). The parallel technique is faster for small (e.g., <500 gates) "highly sequential" circuits or for small numbers of simulated faults. The storage required for a parallel simulator, however, can always be less than that required for a deductive simulator. In general, if sufficient memory is available, the deductive simulator is the more cost-effective simulator when a wide range of circuits is to be simulated and only one type of simulator is available. A substantial savings in logic circuit development cost can be realized when the proper simulation technique is used for logic design verification, fault analysis, and the generation of diagnostic data.

The RAlX (R = Light rare earth; X = Ge, Si) compounds, as a family of magnetic Weyl semimetal, have recently attracted growing attention due to the tunability of Weyl nodes and its interactions with diverse magnetism by rare-earth atoms. Here, we report the magnetotransport evidence and electronic structure calculations on nontrivial band topology of SmAlSi, a new member of this family. At low temperatures, SmAlSi exhibits large non-saturated magnetoresistance (MR) (as large as ∼5500% at 2 K and 48 T) and distinct Shubnikov–de Haas (SdH) oscillations. The field dependent MRs at 2 K deviate from the semiclassical (μ 0 H)2 variation but follow the power-law relation MR ∝ (μ 0 H) m with a crossover from m ∼ 1.52 at low fields (μ 0 H< 15 T) to m ∼ 1 under high fields (μ 0 H> 18 T), which is attributed to the existence of Weyl points and electron–hole compensated characteristics with high mobility. From the analysis of SdH oscillations, two fundamental frequencies originating from the Fermi surface pockets with non-trivial π Berry phases and small cyclotron mass can be identified, this feature is supported by the calculated electronic band structures with two Weyl pockets near the Fermi level. Our study establishes SmAlSi as a paradigm for researching the novel topological states of RAlX family.

ABSTRACTThe question of valence of Cu and rare-earth atoms in the newly discovered oxide superconductors with high transition temperatures is crucial to the understanding of their electronic structure. We have measured the X-Ray Absorption Near Edge Structure (XANES) of Cu K transition and Pr Ljjj transition to obtain information on the valence of Cu, and Pr in La2−xSrxCuO4 and Y1−xPrxBa2Cu3O7-δ. We will present the experimental results, compare them with calculations of absorption cross-section for model atomic clusters, and discuss the valence of Cu as a function of oxygen concentration.

The efficiency of optical trapping is determined by the atomic dynamic dipole polarizability, whose real and imaginary parts are associated with the potential energy and photon-scattering rate respectively. In this article we develop a formalism to calculate analytically the real and imaginary parts of the scalar, vector and tensor polarizabilities of lanthanide atoms. We assume that the sum-over-state formula only comprises transitions involving electrons in the valence orbitals like $6s$, $5d$, $6p$ or $7s$, while transitions involving $4f$ core electrons are neglected. Applying this formalism to the ground level of configuration $4f^q6s^2$, we restrict the sum to transitions implying the $4f^q6s6p$ configuration, which yields polarizabilities depending on two parameters: an effective transition energy and an effective transition dipole moment. Then, by introducing configuration-interaction mixing between $4f^q6s6p$ and other configurations, we demonstrate that the imaginary part of the scalar, vector and tensor polarizabilities is very sensitive to configuration-interaction coefficients, whereas the real part is not. The magnitude and anisotropy of the photon-scattering rate is thus strongly related to the details of the atomic electronic structure. Those analytical results agree with our detailed electronic-structure calculations of energy levels, Land\'e $g$-factors, transition probabilities, polarizabilities and van der Waals $C_6$ coefficients, previously performed on erbium and dysprosium, and presently performed on holmium. Our results show that, although the density of states decreases with increasing $q$, the configuration interaction between $4f^q6s6p$, $4f^{q-1}5d6s^2$ and $4f^{q-1}5d^26s$ is surprisingly stronger in erbium ($q=12$), than in holmium ($q=11$), itself stronger than in dysprosium ($q=10$).